How Logical is Logic?

[Kyrisch]

In the classic dialogue between Achilles and the Tortoise by Lewis Carroll, it is shown that that logic works is a premise that cannot ever be demonstrated or proven because proofs require the use of logic; such proofs might be internally consistent, but would invariably be circular.

 

Now, it's clear that logic is necessary to function sanely in the world. It is also so deeply ingrained that you're probably trying to think of a reason why logic is inescapable, but must stop yourself because you've already begun a process of logical deduction without even realising.

 

So the best we can come up with is internal consistency in the form of:

 

1) In order to live sanely and to make sense of the world, logic must be utilized, and

 

2) logic is so deeply ingrained in our thought processes that we use it without being conscious of its use, so to avoid hypocrisy it must be applied in all cases.

 

(Keeping in mind, of course, that these statements are logical constructs)

 

But self-consistency is supremely unsatisfying. I mean, even the most ludicrous forms religion are self-consistent. The only reason many religions remain so strong is because they make sense within their own framework (although even some necessary doublethink doesn't decrease the fitness of a religion too much). For example, it is nearly impossible to challenge religious precepts on the grounds of religion because they are not falsifiable (i.e. internally consistent).

 

(Oh, are we not allowed to talk about religion again? Read "religions" as "belief systems which ignore outside reality" xP)

 

Regardless, this whole "internal consistency" thing reeks of circular logic. And true, an internally consistent system (that may be externally inconsistent) is better than one that is internally inconsistent (containing, for example, cases of doublethink), but it is still unsettling to me. Then again, the only alternative to logic is a complete disregard thereof, but then you start speaking in Zen-Buddhist Koans: "What is Buddha? Three pounds of flax."

 

 

Thoughts?

Edited June 24, 2009 by Kyrisch

[Daecon]

Logic is rational.

[Sisyphus]

I would go beyond just formal logic and say "reason" more generally. It is possible to be convinced of the blatantly illogical, but in doing so one must of necessity implicitly believe that one's own power of reason has some use as a means to distinguish more true from less true, reality from unreality, etc. We are incapable of doing otherwise. And, to suppose otherwise is, as you say, a self-defeating hypothesis. It cannot be disproven, but it ends the conversation, as any further exploration requires the assumption of its falsehood.

[Dr.]

I believe what the post above me is saying is that a person in a state of conjecture mistakes an image for reality. ? correct me if I'm wrong.

[Mokele]

Logic itself is inductive, since we got all the rules from observing what works and what doesn't. In that sense, logic is as true as anything we sense, and the only way out of it is arguing that we're all dreaming or in the Matrix (which is a load of pseudo-deep crap).

[bascule]

In the classic dialogue between Achilles and the Tortoise by Lewis Carroll, it is shown that that logic works is a premise that cannot ever be demonstrated or proven because proofs require the use of logic

 

The fact that the digital computer you're sitting at works at all is a pretty good testament to the validity of logic.

[CharonY]

Logical statements depend on the validity of the given premises. If the latter are wrong, logical inductions based on these are also invalid.

[iNow]

Logical statements depend on the validity of the given premises. If the latter are wrong, logical inductions based on these are also invalid.

 

In the vast majority of instances, yes. This is absolutely correct. However, there is a small, but non-zero chance that, despite false premises, the conclusions may still be correct. However, these rare instances tend to be a function of coincidence and chance, and are in no way related to a valid/logical induction from the premises.

[Kyrisch]

The fact that the digital computer you're sitting at works at all is a pretty good testament to the validity of logic.

 

Yes, I realized this: that science works is a sign that logic is externally consistent with materialism [empiricism]. But materialism is also an assumption we take for granted (although, like logic, it would be impossible to operate without).

[jimmydasaint]

Just two questions please to clarify what you guys are saying:

1. What do you mean by induction,

2. When is any initial hypothesis free of value ascribed to it by the 'hypothesiser'?

Thanks

[Mokele]

Inductive logic is based on experience or outside data, such as "the sun rose in the east every time it's been observed, therefore it's highly unlikely it will depart from that pattern". Deductive logic is stuff like "If all A are B, and some B are C, then some A are C". Deductive logic can be absolutely certain (and is essentially mathematical), but it depends on the starting assumptions. Inductive logic has a hard time proving or disproving, but typically has fewer assumptions and relies more on external observation.

 

Consider "There are no white ravens". Deductive logic would address it by assessing what a 'raven' is, whether color is a necessary part of the description, and whether potential ravens count. Inductive logic would either say "We looked at a lot of ravens and didn't find any white ones, so they likely don't exist" (leaving open the possibility that they're just very rare or were overlooked) or "We found one, so that's wrong".

[Kyrisch]

Deductive logic is stuff like "If all A are B, and some B are C, then some A are C". Deductive logic can be absolutely certain...

 

So you argue that the tortoise's position in the story I linked to is essentially untenable?

[GutZ]

You can make anything logical so long as you set up axioms properly. If you want your logic to remain in reality you have to match against it. I would say it's like have a bunch of paths (tree like if you want) on a piece of paper. On see through sheet you place another pile of paths.

 

You're trying to place your top sheet (your logic) over the bottom sheet (universe's logic) and have them match. I think that's what science is essentially.

 

Some people don't put their logic up against anything so it is logical in sense but if you were to ask does it hold up to reality? No.

 

Religious people believe there is more to the bottom sheet so they exclude it...but by that same token you have to exclude the top part and accept that basically you have faith, and there is no proving it with any set of logic.